2. The average weight of 100 sold chicken is 3 kilos. The standard deviation of the weights of all the chicken in the store is 1.1 kilos and an 85% level of confidence is to be used. What is the length of the confidence interval?*A. 0.3168B. 0.4268C. 0.51268D. 0.65168
Question
2. The average weight of 100 sold chicken is 3 kilos. The standard deviation of the weights of all the chicken in the store is 1.1 kilos and an 85% level of confidence is to be used. What is the length of the confidence interval?*A. 0.3168B. 0.4268C. 0.51268D. 0.65168
Solution
To calculate the length of the confidence interval, we first need to find the standard error. The standard error (SE) is calculated by dividing the standard deviation (SD) by the square root of the sample size (n). In this case, SD = 1.1 kilos and n = 100.
SE = SD / sqrt(n) = 1.1 / sqrt(100) = 1.1 / 10 = 0.11
Next, we need to find the z-score for an 85% confidence level. The z-score for an 85% confidence level is approximately 1.44 (you can find this value in a standard z-table or use a calculator that provides this value).
The length of the confidence interval is calculated by multiplying the z-score by the standard error.
Length = Z * SE = 1.44 * 0.11 = 0.1584
However, since the confidence interval is two-sided (it includes values above and below the mean), we need to double this value.
So, the length of the confidence interval is 0.1584 * 2 = 0.3168
Therefore, the correct answer is A. 0.3168.
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